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                <h2 id="树的优点"><a href="#树的优点" class="headerlink" title="树的优点"></a>树的优点</h2><p><img src="https://img-blog.csdnimg.cn/d805c482b0e24b5c8e1a62d568473627.png" alt="在这里插入图片描述"></p>
<h1 id="二叉树"><a href="#二叉树" class="headerlink" title="二叉树"></a>二叉树</h1><p><img src="https://img-blog.csdnimg.cn/8776c85d04bb436584b2b05f99871086.png" alt="在这里插入图片描述"></p>
<h2 id="中序查找"><a href="#中序查找" class="headerlink" title="中序查找"></a>中序查找</h2><pre class=" language-java"><code class="language-java"><span class="token keyword">public</span> HeroNode <span class="token function">asd</span><span class="token punctuation">(</span><span class="token keyword">int</span> a<span class="token punctuation">)</span><span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
        <span class="token keyword">if</span><span class="token punctuation">(</span><span class="token keyword">this</span><span class="token punctuation">.</span>no<span class="token operator">==</span>a<span class="token punctuation">)</span><span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
            <span class="token keyword">return</span> <span class="token keyword">this</span><span class="token punctuation">;</span>
        <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
        HeroNode heroNode<span class="token operator">=</span>null<span class="token punctuation">;</span>
        <span class="token keyword">if</span><span class="token punctuation">(</span><span class="token keyword">this</span><span class="token punctuation">.</span>left<span class="token operator">!=</span>null<span class="token punctuation">)</span><span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
            heroNode<span class="token operator">=</span><span class="token keyword">this</span><span class="token punctuation">.</span>left<span class="token punctuation">.</span><span class="token function">asd</span><span class="token punctuation">(</span>a<span class="token punctuation">)</span><span class="token punctuation">;</span>
        <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
        <span class="token keyword">if</span><span class="token punctuation">(</span>heroNode<span class="token operator">!=</span>null<span class="token punctuation">)</span><span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
            <span class="token keyword">return</span> heroNode<span class="token punctuation">;</span>
        <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
        <span class="token keyword">if</span><span class="token punctuation">(</span>right<span class="token operator">!=</span>null<span class="token punctuation">)</span><span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
            heroNode<span class="token operator">=</span><span class="token keyword">this</span><span class="token punctuation">.</span>right<span class="token punctuation">.</span><span class="token function">asd</span><span class="token punctuation">(</span>a<span class="token punctuation">)</span><span class="token punctuation">;</span>
        <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
        <span class="token keyword">return</span> heroNode<span class="token punctuation">;</span>
    <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
</code></pre>
<h2 id="操作与递归分开"><a href="#操作与递归分开" class="headerlink" title="操作与递归分开"></a>操作与递归分开</h2><p><img src="https://img-blog.csdnimg.cn/2d6eeb39bc5e42cc841a185da4e4713b.png" alt="在这里插入图片描述"></p>
<pre class=" language-java"><code class="language-java"><span class="token keyword">class</span> <span class="token class-name">ArrBinaryTree</span><span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
    <span class="token keyword">public</span> <span class="token function">ArrBinaryTree</span><span class="token punctuation">(</span><span class="token keyword">int</span><span class="token punctuation">[</span><span class="token punctuation">]</span> arr<span class="token punctuation">)</span> <span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
        <span class="token keyword">this</span><span class="token punctuation">.</span>arr <span class="token operator">=</span> arr<span class="token punctuation">;</span>
    <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
    <span class="token keyword">private</span> <span class="token keyword">int</span><span class="token punctuation">[</span><span class="token punctuation">]</span> arr<span class="token punctuation">;</span>
    <span class="token keyword">public</span> <span class="token keyword">void</span> <span class="token function">preOrder</span><span class="token punctuation">(</span><span class="token keyword">int</span> index<span class="token punctuation">)</span><span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
        System<span class="token punctuation">.</span>out<span class="token punctuation">.</span><span class="token function">println</span><span class="token punctuation">(</span>arr<span class="token punctuation">[</span>index<span class="token punctuation">]</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
        <span class="token keyword">if</span><span class="token punctuation">(</span><span class="token punctuation">(</span>index<span class="token operator">*</span><span class="token number">2</span><span class="token operator">+</span><span class="token number">1</span><span class="token punctuation">)</span><span class="token operator">&lt;</span>arr<span class="token punctuation">.</span>length<span class="token punctuation">)</span><span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
            <span class="token function">preOrder</span><span class="token punctuation">(</span><span class="token number">2</span><span class="token operator">*</span>index<span class="token operator">+</span><span class="token number">1</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
        <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
        <span class="token keyword">if</span><span class="token punctuation">(</span><span class="token punctuation">(</span>index<span class="token operator">*</span><span class="token number">2</span><span class="token operator">+</span><span class="token number">2</span><span class="token punctuation">)</span><span class="token operator">&lt;</span>arr<span class="token punctuation">.</span>length<span class="token punctuation">)</span><span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
            <span class="token function">preOrder</span><span class="token punctuation">(</span><span class="token number">2</span><span class="token operator">*</span>index<span class="token operator">+</span><span class="token number">2</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
        <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
    <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
<span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
</code></pre>
<p><img src="https://img-blog.csdnimg.cn/2b572e5933f8493a9d89f62c04121732.png" alt="在这里插入图片描述"></p>
<h2 id="线索化二叉树的创建"><a href="#线索化二叉树的创建" class="headerlink" title="线索化二叉树的创建"></a><strong>线索化二叉树的创建</strong></h2><pre class=" language-java"><code class="language-java">  <span class="token keyword">public</span> <span class="token keyword">void</span> <span class="token function">threadNode</span><span class="token punctuation">(</span>HeroNo node<span class="token punctuation">)</span><span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
        <span class="token keyword">if</span><span class="token punctuation">(</span>node<span class="token operator">==</span>null<span class="token punctuation">)</span><span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
            <span class="token keyword">return</span><span class="token punctuation">;</span>
        <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
        <span class="token function">threadNode</span><span class="token punctuation">(</span>node<span class="token punctuation">.</span><span class="token function">getLeft</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">;</span>

        <span class="token keyword">if</span><span class="token punctuation">(</span>node<span class="token punctuation">.</span><span class="token function">getLeft</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token operator">==</span>null<span class="token punctuation">)</span><span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
            node<span class="token punctuation">.</span><span class="token function">setLeft</span><span class="token punctuation">(</span>pre<span class="token punctuation">)</span><span class="token punctuation">;</span>
            node<span class="token punctuation">.</span><span class="token function">setLeftType</span><span class="token punctuation">(</span><span class="token number">1</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
        <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
        <span class="token keyword">if</span><span class="token punctuation">(</span>pre<span class="token operator">!=</span>null<span class="token operator">&amp;&amp;</span>pre<span class="token punctuation">.</span><span class="token function">getRight</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token operator">==</span>null<span class="token punctuation">)</span><span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
            pre<span class="token punctuation">.</span><span class="token function">setRight</span><span class="token punctuation">(</span>node<span class="token punctuation">)</span><span class="token punctuation">;</span>
            pre<span class="token punctuation">.</span><span class="token function">setRightType</span><span class="token punctuation">(</span><span class="token number">1</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
        <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
        pre<span class="token operator">=</span>node<span class="token punctuation">;</span>
        <span class="token function">threadNode</span><span class="token punctuation">(</span>node<span class="token punctuation">.</span><span class="token function">getRight</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
    <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
</code></pre>
<h2 id="中序线索化二叉树遍历"><a href="#中序线索化二叉树遍历" class="headerlink" title="中序线索化二叉树遍历"></a><strong>中序线索化二叉树遍历</strong></h2><pre class=" language-java"><code class="language-java">   <span class="token keyword">public</span> <span class="token keyword">void</span> <span class="token function">threadedList</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
        HeroNo no<span class="token operator">=</span>heroNo<span class="token punctuation">;</span>
        <span class="token keyword">while</span> <span class="token punctuation">(</span>no<span class="token operator">!=</span>null<span class="token punctuation">)</span><span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
            <span class="token keyword">while</span> <span class="token punctuation">(</span>no<span class="token punctuation">.</span><span class="token function">getLeftType</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token operator">!=</span><span class="token number">1</span><span class="token punctuation">)</span><span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
                no<span class="token operator">=</span>no<span class="token punctuation">.</span><span class="token function">getLeft</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
            <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
            System<span class="token punctuation">.</span>out<span class="token punctuation">.</span><span class="token function">println</span><span class="token punctuation">(</span>no<span class="token punctuation">.</span><span class="token function">getNo</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
            <span class="token keyword">while</span> <span class="token punctuation">(</span>no<span class="token punctuation">.</span><span class="token function">getRightType</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token operator">==</span><span class="token number">1</span><span class="token punctuation">)</span><span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
                no<span class="token operator">=</span>no<span class="token punctuation">.</span><span class="token function">getRight</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
                System<span class="token punctuation">.</span>out<span class="token punctuation">.</span><span class="token function">println</span><span class="token punctuation">(</span>no<span class="token punctuation">.</span><span class="token function">getNo</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
            <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
            no<span class="token operator">=</span>no<span class="token punctuation">.</span><span class="token function">getRight</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
        <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
    <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
</code></pre>
<h2 id="堆排序"><a href="#堆排序" class="headerlink" title="堆排序"></a>堆排序</h2><p><img src="https://img-blog.csdnimg.cn/5d96495e28c2462e8fcf72fed88b8ff5.png" alt="在这里插入图片描述"><br><strong>一般升序用大顶堆，降序用小顶堆</strong><br><img src="https://img-blog.csdnimg.cn/b295976a8e594145a2a0a213dd8417bf.png" alt="在这里插入图片描述"></p>
<pre class=" language-java"><code class="language-java"><span class="token keyword">public</span> <span class="token keyword">class</span> <span class="token class-name">text22</span> <span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
    <span class="token keyword">public</span> <span class="token keyword">static</span> <span class="token keyword">void</span> <span class="token function">main</span><span class="token punctuation">(</span>String<span class="token punctuation">[</span><span class="token punctuation">]</span> args<span class="token punctuation">)</span> <span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
        <span class="token keyword">int</span><span class="token punctuation">[</span><span class="token punctuation">]</span> arr<span class="token operator">=</span><span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span><span class="token number">4</span><span class="token punctuation">,</span><span class="token number">6</span><span class="token punctuation">,</span><span class="token number">8</span><span class="token punctuation">,</span><span class="token number">5</span><span class="token punctuation">,</span><span class="token number">9</span><span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span><span class="token punctuation">;</span>
        <span class="token function">heapSort</span><span class="token punctuation">(</span>arr<span class="token punctuation">)</span><span class="token punctuation">;</span>
    <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
    <span class="token keyword">public</span> <span class="token keyword">static</span> <span class="token keyword">void</span> <span class="token function">heapSort</span><span class="token punctuation">(</span><span class="token keyword">int</span><span class="token punctuation">[</span><span class="token punctuation">]</span> arr<span class="token punctuation">)</span><span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
        <span class="token keyword">int</span> temp<span class="token punctuation">;</span>
        <span class="token keyword">for</span><span class="token punctuation">(</span><span class="token keyword">int</span> i<span class="token operator">=</span>arr<span class="token punctuation">.</span>length<span class="token operator">/</span><span class="token number">2</span><span class="token operator">-</span><span class="token number">1</span><span class="token punctuation">;</span>i<span class="token operator">>=</span><span class="token number">0</span><span class="token punctuation">;</span>i<span class="token operator">--</span><span class="token punctuation">)</span><span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
            <span class="token function">adjust</span><span class="token punctuation">(</span>arr<span class="token punctuation">,</span>i<span class="token punctuation">,</span>arr<span class="token punctuation">.</span>length<span class="token punctuation">)</span><span class="token punctuation">;</span>
        <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
        <span class="token keyword">for</span><span class="token punctuation">(</span><span class="token keyword">int</span> j<span class="token operator">=</span>arr<span class="token punctuation">.</span>length<span class="token operator">-</span><span class="token number">1</span><span class="token punctuation">;</span>j<span class="token operator">></span><span class="token number">0</span><span class="token punctuation">;</span>j<span class="token operator">--</span><span class="token punctuation">)</span><span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
            temp<span class="token operator">=</span>arr<span class="token punctuation">[</span>j<span class="token punctuation">]</span><span class="token punctuation">;</span>
            arr<span class="token punctuation">[</span>j<span class="token punctuation">]</span><span class="token operator">=</span>arr<span class="token punctuation">[</span><span class="token number">0</span><span class="token punctuation">]</span><span class="token punctuation">;</span>
            arr<span class="token punctuation">[</span><span class="token number">0</span><span class="token punctuation">]</span><span class="token operator">=</span>temp<span class="token punctuation">;</span>
            <span class="token function">adjust</span><span class="token punctuation">(</span>arr<span class="token punctuation">,</span><span class="token number">0</span><span class="token punctuation">,</span>j<span class="token punctuation">)</span><span class="token punctuation">;</span>
        <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>

        System<span class="token punctuation">.</span>out<span class="token punctuation">.</span><span class="token function">println</span><span class="token punctuation">(</span>Arrays<span class="token punctuation">.</span><span class="token function">toString</span><span class="token punctuation">(</span>arr<span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
    <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
    <span class="token keyword">public</span> <span class="token keyword">static</span> <span class="token keyword">void</span> <span class="token function">adjust</span><span class="token punctuation">(</span><span class="token keyword">int</span><span class="token punctuation">[</span><span class="token punctuation">]</span> arr<span class="token punctuation">,</span><span class="token keyword">int</span> i<span class="token punctuation">,</span><span class="token keyword">int</span> length<span class="token punctuation">)</span><span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>

        <span class="token keyword">int</span> temp<span class="token operator">=</span>arr<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">;</span>
        <span class="token keyword">for</span><span class="token punctuation">(</span><span class="token keyword">int</span> k<span class="token operator">=</span>i<span class="token operator">*</span><span class="token number">2</span><span class="token operator">+</span><span class="token number">1</span><span class="token punctuation">;</span>k<span class="token operator">&lt;</span>length<span class="token punctuation">;</span>k<span class="token operator">=</span>k<span class="token operator">*</span><span class="token number">2</span><span class="token operator">+</span><span class="token number">1</span><span class="token punctuation">)</span><span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
            <span class="token keyword">if</span><span class="token punctuation">(</span>k<span class="token operator">+</span><span class="token number">1</span><span class="token operator">&lt;</span>length<span class="token operator">&amp;&amp;</span>arr<span class="token punctuation">[</span>k<span class="token punctuation">]</span><span class="token operator">&lt;</span>arr<span class="token punctuation">[</span>k<span class="token operator">+</span><span class="token number">1</span><span class="token punctuation">]</span><span class="token punctuation">)</span><span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
                k<span class="token operator">++</span><span class="token punctuation">;</span>
            <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
            <span class="token keyword">if</span><span class="token punctuation">(</span>temp<span class="token operator">&lt;</span>arr<span class="token punctuation">[</span>k<span class="token punctuation">]</span><span class="token punctuation">)</span><span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
                arr<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token operator">=</span>arr<span class="token punctuation">[</span>k<span class="token punctuation">]</span><span class="token punctuation">;</span>
                i<span class="token operator">=</span>k<span class="token punctuation">;</span>
            <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span><span class="token keyword">else</span> <span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
                <span class="token keyword">break</span><span class="token punctuation">;</span>
            <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
        <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
        arr<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token operator">=</span>temp<span class="token punctuation">;</span>
    <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
<span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
</code></pre>
<h2 id="赫夫曼树"><a href="#赫夫曼树" class="headerlink" title="赫夫曼树"></a>赫夫曼树</h2><p><img src="https://img-blog.csdnimg.cn/069b9c9f493e43efad4b985eebe1b0ae.png" alt="在这里插入图片描述"><br><img src="https://img-blog.csdnimg.cn/80f99a7de45c4193adb832f37bcbb182.png" alt="在这里插入图片描述"><br><strong>创建赫夫曼树</strong></p>
<pre class=" language-java"><code class="language-java"><span class="token keyword">public</span> <span class="token keyword">class</span> <span class="token class-name">text23</span> <span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
    <span class="token keyword">public</span> <span class="token keyword">static</span> <span class="token keyword">void</span> <span class="token function">main</span><span class="token punctuation">(</span>String<span class="token punctuation">[</span><span class="token punctuation">]</span> args<span class="token punctuation">)</span> <span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
        <span class="token keyword">int</span><span class="token punctuation">[</span><span class="token punctuation">]</span> arr<span class="token operator">=</span><span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span><span class="token number">13</span><span class="token punctuation">,</span><span class="token number">7</span><span class="token punctuation">,</span><span class="token number">8</span><span class="token punctuation">,</span><span class="token number">3</span><span class="token punctuation">,</span><span class="token number">29</span><span class="token punctuation">,</span><span class="token number">6</span><span class="token punctuation">,</span><span class="token number">1</span><span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span><span class="token punctuation">;</span>
        Node creat <span class="token operator">=</span> <span class="token function">creat</span><span class="token punctuation">(</span>arr<span class="token punctuation">)</span><span class="token punctuation">;</span>
        creat<span class="token punctuation">.</span><span class="token function">asd</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
    <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
    <span class="token keyword">public</span> <span class="token keyword">static</span> Node <span class="token function">creat</span><span class="token punctuation">(</span><span class="token keyword">int</span><span class="token punctuation">[</span><span class="token punctuation">]</span> arr<span class="token punctuation">)</span><span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
        List<span class="token operator">&lt;</span>Node<span class="token operator">></span> nodes<span class="token operator">=</span><span class="token keyword">new</span> <span class="token class-name">ArrayList</span><span class="token operator">&lt;</span>Node<span class="token operator">></span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
        <span class="token keyword">for</span><span class="token punctuation">(</span><span class="token keyword">int</span> value<span class="token operator">:</span>arr<span class="token punctuation">)</span><span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
            nodes<span class="token punctuation">.</span><span class="token function">add</span><span class="token punctuation">(</span><span class="token keyword">new</span> <span class="token class-name">Node</span><span class="token punctuation">(</span>value<span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
        <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
        <span class="token keyword">while</span> <span class="token punctuation">(</span>nodes<span class="token punctuation">.</span><span class="token function">size</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token operator">></span><span class="token number">1</span><span class="token punctuation">)</span><span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
            Collections<span class="token punctuation">.</span><span class="token function">sort</span><span class="token punctuation">(</span>nodes<span class="token punctuation">)</span><span class="token punctuation">;</span>
            Node node<span class="token operator">=</span>nodes<span class="token punctuation">.</span><span class="token function">get</span><span class="token punctuation">(</span><span class="token number">0</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
            Node node1<span class="token operator">=</span>nodes<span class="token punctuation">.</span><span class="token function">get</span><span class="token punctuation">(</span><span class="token number">1</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
            Node node2<span class="token operator">=</span><span class="token keyword">new</span> <span class="token class-name">Node</span><span class="token punctuation">(</span>node<span class="token punctuation">.</span>value<span class="token operator">+</span>node1<span class="token punctuation">.</span>value<span class="token punctuation">)</span><span class="token punctuation">;</span>
            node2<span class="token punctuation">.</span>left<span class="token operator">=</span>node<span class="token punctuation">;</span>
            node2<span class="token punctuation">.</span>right<span class="token operator">=</span>node1<span class="token punctuation">;</span>
            nodes<span class="token punctuation">.</span><span class="token function">remove</span><span class="token punctuation">(</span>node<span class="token punctuation">)</span><span class="token punctuation">;</span>
            nodes<span class="token punctuation">.</span><span class="token function">remove</span><span class="token punctuation">(</span>node1<span class="token punctuation">)</span><span class="token punctuation">;</span>
            nodes<span class="token punctuation">.</span><span class="token function">add</span><span class="token punctuation">(</span>node2<span class="token punctuation">)</span><span class="token punctuation">;</span>
        <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
        <span class="token keyword">return</span> nodes<span class="token punctuation">.</span><span class="token function">get</span><span class="token punctuation">(</span><span class="token number">0</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
    <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
<span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
<span class="token keyword">class</span> <span class="token class-name">Node</span> <span class="token keyword">implements</span> <span class="token class-name">Comparable</span><span class="token operator">&lt;</span>Node<span class="token operator">></span><span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
    <span class="token keyword">int</span> value<span class="token punctuation">;</span>
    Node left<span class="token punctuation">;</span>
    Node right<span class="token punctuation">;</span>

    <span class="token keyword">public</span> <span class="token function">Node</span><span class="token punctuation">(</span><span class="token keyword">int</span> value<span class="token punctuation">)</span> <span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
        <span class="token keyword">this</span><span class="token punctuation">.</span>value <span class="token operator">=</span> value<span class="token punctuation">;</span>
    <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>

    <span class="token annotation punctuation">@Override</span>
    <span class="token keyword">public</span> <span class="token keyword">int</span> <span class="token function">compareTo</span><span class="token punctuation">(</span>Node o<span class="token punctuation">)</span> <span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
        <span class="token keyword">return</span> <span class="token keyword">this</span><span class="token punctuation">.</span>value<span class="token operator">-</span>o<span class="token punctuation">.</span>value<span class="token punctuation">;</span>
    <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
    <span class="token keyword">public</span> <span class="token keyword">void</span> <span class="token function">asd</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
        <span class="token keyword">if</span><span class="token punctuation">(</span><span class="token keyword">this</span><span class="token operator">!=</span>null<span class="token punctuation">)</span> <span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
            System<span class="token punctuation">.</span>out<span class="token punctuation">.</span><span class="token function">println</span><span class="token punctuation">(</span><span class="token keyword">this</span><span class="token punctuation">.</span>value<span class="token punctuation">)</span><span class="token punctuation">;</span>
            <span class="token keyword">if</span><span class="token punctuation">(</span><span class="token keyword">this</span><span class="token punctuation">.</span>left<span class="token operator">!=</span>null<span class="token punctuation">)</span> <span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
                <span class="token keyword">this</span><span class="token punctuation">.</span>left<span class="token punctuation">.</span><span class="token function">asd</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
            <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
            <span class="token keyword">if</span><span class="token punctuation">(</span><span class="token keyword">this</span><span class="token punctuation">.</span>right<span class="token operator">!=</span>null<span class="token punctuation">)</span> <span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
                <span class="token keyword">this</span><span class="token punctuation">.</span>right<span class="token punctuation">.</span><span class="token function">asd</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
            <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
        <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span><span class="token keyword">else</span> <span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
            <span class="token keyword">return</span><span class="token punctuation">;</span>
        <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
    <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
<span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
</code></pre>
<h2 id="赫夫曼编码"><a href="#赫夫曼编码" class="headerlink" title="赫夫曼编码"></a>赫夫曼编码</h2><p><img src="https://img-blog.csdnimg.cn/4bf95006082348e08d2d1673a69c1c6c.png" alt="在这里插入图片描述"><br><strong>生成赫夫曼编码</strong></p>
<pre class=" language-java"><code class="language-java"><span class="token keyword">public</span> <span class="token keyword">class</span> <span class="token class-name">text24</span> <span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
    <span class="token keyword">public</span> <span class="token keyword">static</span> <span class="token keyword">void</span> <span class="token function">main</span><span class="token punctuation">(</span>String<span class="token punctuation">[</span><span class="token punctuation">]</span> args<span class="token punctuation">)</span> <span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
        String str<span class="token operator">=</span><span class="token string">"i like like like java do you like a java"</span><span class="token punctuation">;</span>
        <span class="token keyword">byte</span><span class="token punctuation">[</span><span class="token punctuation">]</span> contentBytes<span class="token operator">=</span>str<span class="token punctuation">.</span><span class="token function">getBytes</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
        List<span class="token operator">&lt;</span>Node1<span class="token operator">></span> nodes <span class="token operator">=</span> <span class="token function">getNodes</span><span class="token punctuation">(</span>contentBytes<span class="token punctuation">)</span><span class="token punctuation">;</span>
        Node1 node1 <span class="token operator">=</span> <span class="token function">create</span><span class="token punctuation">(</span>nodes<span class="token punctuation">)</span><span class="token punctuation">;</span>
        <span class="token function">getCodes</span><span class="token punctuation">(</span>node1<span class="token punctuation">,</span><span class="token string">""</span><span class="token punctuation">,</span><span class="token string">""</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
        System<span class="token punctuation">.</span>out<span class="token punctuation">.</span><span class="token function">println</span><span class="token punctuation">(</span>huff<span class="token punctuation">)</span><span class="token punctuation">;</span>
    <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
    <span class="token keyword">static</span> Map<span class="token operator">&lt;</span>Byte<span class="token punctuation">,</span>String<span class="token operator">></span> huff<span class="token operator">=</span><span class="token keyword">new</span> <span class="token class-name">HashMap</span><span class="token operator">&lt;</span><span class="token operator">></span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
    <span class="token keyword">private</span> <span class="token keyword">static</span> <span class="token keyword">void</span> <span class="token function">getCodes</span><span class="token punctuation">(</span>Node1 node<span class="token punctuation">,</span>String code<span class="token punctuation">,</span>String asd<span class="token punctuation">)</span><span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
        asd<span class="token operator">=</span>asd<span class="token punctuation">.</span><span class="token function">concat</span><span class="token punctuation">(</span>code<span class="token punctuation">)</span><span class="token punctuation">;</span>
        <span class="token keyword">if</span><span class="token punctuation">(</span>node<span class="token punctuation">.</span>data<span class="token operator">==</span>null<span class="token punctuation">)</span><span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
            <span class="token function">getCodes</span><span class="token punctuation">(</span>node<span class="token punctuation">.</span>left<span class="token punctuation">,</span><span class="token string">"0"</span><span class="token punctuation">,</span>asd<span class="token punctuation">)</span><span class="token punctuation">;</span>
            <span class="token function">getCodes</span><span class="token punctuation">(</span>node<span class="token punctuation">.</span>right<span class="token punctuation">,</span><span class="token string">"1"</span><span class="token punctuation">,</span>asd<span class="token punctuation">)</span><span class="token punctuation">;</span>
        <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span><span class="token keyword">else</span> <span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
            huff<span class="token punctuation">.</span><span class="token function">put</span><span class="token punctuation">(</span>node<span class="token punctuation">.</span>data<span class="token punctuation">,</span>asd<span class="token punctuation">)</span><span class="token punctuation">;</span>
            <span class="token keyword">return</span><span class="token punctuation">;</span>
        <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
    <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
    
    <span class="token keyword">private</span> <span class="token keyword">static</span> List<span class="token operator">&lt;</span>Node1<span class="token operator">></span> <span class="token function">getNodes</span><span class="token punctuation">(</span><span class="token keyword">byte</span><span class="token punctuation">[</span><span class="token punctuation">]</span> bytes<span class="token punctuation">)</span><span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
        ArrayList<span class="token operator">&lt;</span>Node1<span class="token operator">></span> nodes <span class="token operator">=</span> <span class="token keyword">new</span> <span class="token class-name">ArrayList</span><span class="token operator">&lt;</span><span class="token operator">></span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
        HashMap<span class="token operator">&lt;</span>Byte<span class="token punctuation">,</span> Integer<span class="token operator">></span> map <span class="token operator">=</span> <span class="token keyword">new</span> <span class="token class-name">HashMap</span><span class="token operator">&lt;</span><span class="token operator">></span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
        <span class="token keyword">for</span><span class="token punctuation">(</span><span class="token keyword">byte</span> b<span class="token operator">:</span>bytes<span class="token punctuation">)</span><span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
            Integer count<span class="token operator">=</span>map<span class="token punctuation">.</span><span class="token function">get</span><span class="token punctuation">(</span>b<span class="token punctuation">)</span><span class="token punctuation">;</span>
            <span class="token keyword">if</span><span class="token punctuation">(</span>count<span class="token operator">==</span>null<span class="token punctuation">)</span><span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
                map<span class="token punctuation">.</span><span class="token function">put</span><span class="token punctuation">(</span>b<span class="token punctuation">,</span><span class="token number">1</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
            <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span><span class="token keyword">else</span> <span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
                map<span class="token punctuation">.</span><span class="token function">put</span><span class="token punctuation">(</span>b<span class="token punctuation">,</span>count<span class="token operator">+</span><span class="token number">1</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
            <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
        <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
        <span class="token keyword">for</span><span class="token punctuation">(</span>Map<span class="token punctuation">.</span>Entry<span class="token operator">&lt;</span>Byte<span class="token punctuation">,</span>Integer<span class="token operator">></span> entry<span class="token operator">:</span>map<span class="token punctuation">.</span><span class="token function">entrySet</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
            nodes<span class="token punctuation">.</span><span class="token function">add</span><span class="token punctuation">(</span><span class="token keyword">new</span> <span class="token class-name">Node1</span><span class="token punctuation">(</span>entry<span class="token punctuation">.</span><span class="token function">getKey</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">,</span>entry<span class="token punctuation">.</span><span class="token function">getValue</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
        <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
        <span class="token keyword">return</span> nodes<span class="token punctuation">;</span>
    <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
    <span class="token keyword">private</span> <span class="token keyword">static</span> Node1 <span class="token function">create</span><span class="token punctuation">(</span>List<span class="token operator">&lt;</span>Node1<span class="token operator">></span> node1s<span class="token punctuation">)</span><span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
        <span class="token keyword">while</span> <span class="token punctuation">(</span>node1s<span class="token punctuation">.</span><span class="token function">size</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token operator">></span><span class="token number">1</span><span class="token punctuation">)</span><span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
            Collections<span class="token punctuation">.</span><span class="token function">sort</span><span class="token punctuation">(</span>node1s<span class="token punctuation">)</span><span class="token punctuation">;</span>
            Node1 node1 <span class="token operator">=</span> node1s<span class="token punctuation">.</span><span class="token function">get</span><span class="token punctuation">(</span><span class="token number">0</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
            Node1 node11 <span class="token operator">=</span> node1s<span class="token punctuation">.</span><span class="token function">get</span><span class="token punctuation">(</span><span class="token number">1</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
            Node1 node12<span class="token operator">=</span><span class="token keyword">new</span> <span class="token class-name">Node1</span><span class="token punctuation">(</span>null<span class="token punctuation">,</span>node1<span class="token punctuation">.</span>weight<span class="token operator">+</span>node11<span class="token punctuation">.</span>weight<span class="token punctuation">)</span><span class="token punctuation">;</span>
            node12<span class="token punctuation">.</span>left<span class="token operator">=</span>node1<span class="token punctuation">;</span>
            node12<span class="token punctuation">.</span>right<span class="token operator">=</span>node11<span class="token punctuation">;</span>
            node1s<span class="token punctuation">.</span><span class="token function">remove</span><span class="token punctuation">(</span>node1<span class="token punctuation">)</span><span class="token punctuation">;</span>
            node1s<span class="token punctuation">.</span><span class="token function">remove</span><span class="token punctuation">(</span>node11<span class="token punctuation">)</span><span class="token punctuation">;</span>
            node1s<span class="token punctuation">.</span><span class="token function">add</span><span class="token punctuation">(</span>node12<span class="token punctuation">)</span><span class="token punctuation">;</span>
        <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
        <span class="token keyword">return</span> node1s<span class="token punctuation">.</span><span class="token function">get</span><span class="token punctuation">(</span><span class="token number">0</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
    <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
<span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
<span class="token keyword">class</span> <span class="token class-name">Node1</span> <span class="token keyword">implements</span> <span class="token class-name">Comparable</span><span class="token operator">&lt;</span>Node1<span class="token operator">></span><span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
    Byte data<span class="token punctuation">;</span>
    <span class="token keyword">int</span> weight<span class="token punctuation">;</span>
    Node1 left<span class="token punctuation">;</span>
    Node1 right<span class="token punctuation">;</span>

    <span class="token keyword">public</span> <span class="token function">Node1</span><span class="token punctuation">(</span>Byte data<span class="token punctuation">,</span> <span class="token keyword">int</span> weight<span class="token punctuation">)</span> <span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
        <span class="token keyword">this</span><span class="token punctuation">.</span>data <span class="token operator">=</span> data<span class="token punctuation">;</span>
        <span class="token keyword">this</span><span class="token punctuation">.</span>weight <span class="token operator">=</span> weight<span class="token punctuation">;</span>
    <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>

    <span class="token annotation punctuation">@Override</span>
    <span class="token keyword">public</span> <span class="token keyword">int</span> <span class="token function">compareTo</span><span class="token punctuation">(</span>Node1 o<span class="token punctuation">)</span> <span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
        <span class="token keyword">return</span> <span class="token keyword">this</span><span class="token punctuation">.</span>weight<span class="token operator">-</span>o<span class="token punctuation">.</span>weight<span class="token punctuation">;</span>
    <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>

    <span class="token annotation punctuation">@Override</span>
    <span class="token keyword">public</span> String <span class="token function">toString</span><span class="token punctuation">(</span><span class="token punctuation">)</span> <span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
        <span class="token keyword">return</span> <span class="token string">"Node1&amp;#123;"</span> <span class="token operator">+</span>
                <span class="token string">"data="</span> <span class="token operator">+</span> data <span class="token operator">+</span>
                <span class="token string">", weight="</span> <span class="token operator">+</span> weight <span class="token operator">+</span>
                <span class="token string">'&amp;#125;'</span><span class="token punctuation">;</span>
    <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
    <span class="token keyword">public</span> <span class="token keyword">void</span> <span class="token function">asd</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
        <span class="token keyword">if</span><span class="token punctuation">(</span><span class="token keyword">this</span><span class="token operator">==</span>null<span class="token punctuation">)</span><span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
            <span class="token keyword">return</span><span class="token punctuation">;</span>
        <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
        System<span class="token punctuation">.</span>out<span class="token punctuation">.</span><span class="token function">println</span><span class="token punctuation">(</span><span class="token keyword">this</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
        <span class="token keyword">if</span><span class="token punctuation">(</span><span class="token keyword">this</span><span class="token punctuation">.</span>left<span class="token operator">!=</span>null<span class="token punctuation">)</span> <span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
            <span class="token keyword">this</span><span class="token punctuation">.</span>left<span class="token punctuation">.</span><span class="token function">asd</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
        <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
        <span class="token keyword">if</span><span class="token punctuation">(</span><span class="token keyword">this</span><span class="token punctuation">.</span>right<span class="token operator">!=</span>null<span class="token punctuation">)</span> <span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
            <span class="token keyword">this</span><span class="token punctuation">.</span>right<span class="token punctuation">.</span><span class="token function">asd</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
        <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
    <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
<span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
</code></pre>
<p><strong>二进制转换成byte</strong></p>
<pre class=" language-java"><code class="language-java"><span class="token keyword">public</span> <span class="token keyword">static</span> <span class="token keyword">void</span> <span class="token function">main</span><span class="token punctuation">(</span>String<span class="token punctuation">[</span><span class="token punctuation">]</span> args<span class="token punctuation">)</span> <span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
        String a<span class="token operator">=</span><span class="token string">"01110101"</span><span class="token punctuation">;</span>
        <span class="token keyword">byte</span> b<span class="token operator">=</span> <span class="token punctuation">(</span><span class="token keyword">byte</span><span class="token punctuation">)</span> Integer<span class="token punctuation">.</span><span class="token function">parseInt</span><span class="token punctuation">(</span>a<span class="token punctuation">,</span><span class="token number">2</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
        System<span class="token punctuation">.</span>out<span class="token punctuation">.</span><span class="token function">println</span><span class="token punctuation">(</span>b<span class="token punctuation">)</span><span class="token punctuation">;</span>
    <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
</code></pre>
<p><strong>数据压缩</strong></p>
<pre class=" language-java"><code class="language-java"><span class="token keyword">private</span> <span class="token keyword">static</span> <span class="token keyword">byte</span><span class="token punctuation">[</span><span class="token punctuation">]</span> <span class="token function">zip</span><span class="token punctuation">(</span><span class="token keyword">byte</span><span class="token punctuation">[</span><span class="token punctuation">]</span> bytes<span class="token punctuation">,</span>Map<span class="token operator">&lt;</span>Byte<span class="token punctuation">,</span>String<span class="token operator">></span> huff<span class="token punctuation">)</span><span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
        StringBuilder stringBuilder<span class="token operator">=</span><span class="token keyword">new</span> <span class="token class-name">StringBuilder</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
        <span class="token keyword">for</span><span class="token punctuation">(</span><span class="token keyword">byte</span> b<span class="token operator">:</span>bytes<span class="token punctuation">)</span><span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
            stringBuilder<span class="token punctuation">.</span><span class="token function">append</span><span class="token punctuation">(</span>huff<span class="token punctuation">.</span><span class="token function">get</span><span class="token punctuation">(</span>b<span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
        <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
        <span class="token keyword">int</span> length<span class="token operator">=</span><span class="token number">0</span><span class="token punctuation">;</span>
        <span class="token keyword">if</span><span class="token punctuation">(</span>stringBuilder<span class="token punctuation">.</span><span class="token function">length</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token operator">%</span><span class="token number">8</span><span class="token operator">==</span><span class="token number">0</span><span class="token punctuation">)</span><span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
            length<span class="token operator">=</span>stringBuilder<span class="token punctuation">.</span><span class="token function">length</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token operator">/</span><span class="token number">8</span><span class="token punctuation">;</span>
        <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span><span class="token keyword">else</span> <span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
            length<span class="token operator">=</span>stringBuilder<span class="token punctuation">.</span><span class="token function">length</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token operator">/</span><span class="token number">8</span><span class="token operator">+</span><span class="token number">1</span><span class="token punctuation">;</span>
        <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
        <span class="token keyword">byte</span><span class="token punctuation">[</span><span class="token punctuation">]</span> bytes1<span class="token operator">=</span><span class="token keyword">new</span> <span class="token class-name">byte</span><span class="token punctuation">[</span>length<span class="token punctuation">]</span><span class="token punctuation">;</span>
        <span class="token keyword">int</span> index<span class="token operator">=</span><span class="token number">0</span><span class="token punctuation">;</span>
        <span class="token keyword">for</span><span class="token punctuation">(</span><span class="token keyword">int</span> i<span class="token operator">=</span><span class="token number">0</span><span class="token punctuation">;</span>i<span class="token operator">&lt;</span>stringBuilder<span class="token punctuation">.</span><span class="token function">length</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>i<span class="token operator">+=</span><span class="token number">8</span><span class="token punctuation">)</span><span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
            <span class="token keyword">if</span><span class="token punctuation">(</span><span class="token punctuation">(</span>i<span class="token operator">+</span><span class="token number">8</span><span class="token punctuation">)</span><span class="token operator">&lt;</span>stringBuilder<span class="token punctuation">.</span><span class="token function">length</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">)</span> <span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
                bytes1<span class="token punctuation">[</span>index<span class="token punctuation">]</span> <span class="token operator">=</span> <span class="token punctuation">(</span><span class="token keyword">byte</span><span class="token punctuation">)</span>Integer<span class="token punctuation">.</span><span class="token function">parseInt</span><span class="token punctuation">(</span>stringBuilder<span class="token punctuation">.</span><span class="token function">substring</span><span class="token punctuation">(</span>i<span class="token punctuation">,</span> i <span class="token operator">+</span> <span class="token number">8</span><span class="token punctuation">)</span><span class="token punctuation">,</span><span class="token number">2</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
            <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span><span class="token keyword">else</span> <span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
                bytes1<span class="token punctuation">[</span>index<span class="token punctuation">]</span> <span class="token operator">=</span> <span class="token punctuation">(</span><span class="token keyword">byte</span><span class="token punctuation">)</span>Integer<span class="token punctuation">.</span><span class="token function">parseInt</span><span class="token punctuation">(</span>stringBuilder<span class="token punctuation">.</span><span class="token function">substring</span><span class="token punctuation">(</span>i<span class="token punctuation">,</span> stringBuilder<span class="token punctuation">.</span><span class="token function">length</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">,</span><span class="token number">2</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
            <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
            index<span class="token operator">++</span><span class="token punctuation">;</span>
        <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
        <span class="token keyword">return</span> bytes1<span class="token punctuation">;</span>
    <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
</code></pre>
<h2 id="二叉排序树"><a href="#二叉排序树" class="headerlink" title="二叉排序树"></a>二叉排序树</h2><p>二叉排序树（BST）：对二叉排序树的任何一个非叶子节点，要求左子节点的值比当前节点的值小，右子节点的值比当前节点的大，如果相同，则放在左子节点或右子节点。</p>
<p><strong>创建和遍历</strong></p>
<pre class=" language-java"><code class="language-java"><span class="token keyword">class</span> <span class="token class-name">Node</span><span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
    <span class="token keyword">int</span> value<span class="token punctuation">;</span>
    Node left<span class="token punctuation">;</span>
    Node right<span class="token punctuation">;</span>
    <span class="token keyword">public</span> <span class="token function">Node</span><span class="token punctuation">(</span><span class="token keyword">int</span> value<span class="token punctuation">)</span><span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
        <span class="token keyword">this</span><span class="token punctuation">.</span>value<span class="token operator">=</span>value<span class="token punctuation">;</span>
    <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
    <span class="token comment" spellcheck="true">//递归的形式添加</span>
    <span class="token keyword">public</span> <span class="token keyword">void</span> <span class="token function">add</span><span class="token punctuation">(</span>Node node<span class="token punctuation">)</span><span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
        <span class="token keyword">if</span><span class="token punctuation">(</span>node<span class="token operator">==</span>null<span class="token punctuation">)</span><span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
            <span class="token keyword">return</span><span class="token punctuation">;</span>
        <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
        <span class="token keyword">if</span><span class="token punctuation">(</span>node<span class="token punctuation">.</span>value<span class="token operator">&lt;</span><span class="token keyword">this</span><span class="token punctuation">.</span>value<span class="token punctuation">)</span><span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
            <span class="token keyword">if</span><span class="token punctuation">(</span><span class="token keyword">this</span><span class="token punctuation">.</span>left<span class="token operator">==</span>null<span class="token punctuation">)</span><span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
                <span class="token keyword">this</span><span class="token punctuation">.</span>left<span class="token operator">=</span>node<span class="token punctuation">;</span>
            <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span><span class="token keyword">else</span> <span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
                <span class="token keyword">this</span><span class="token punctuation">.</span>left<span class="token punctuation">.</span><span class="token function">add</span><span class="token punctuation">(</span>node<span class="token punctuation">)</span><span class="token punctuation">;</span>
            <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
        <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span><span class="token keyword">else</span> <span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
            <span class="token keyword">if</span><span class="token punctuation">(</span><span class="token keyword">this</span><span class="token punctuation">.</span>right<span class="token operator">==</span>null<span class="token punctuation">)</span><span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
                <span class="token keyword">this</span><span class="token punctuation">.</span>right<span class="token operator">=</span>node<span class="token punctuation">;</span>
            <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span><span class="token keyword">else</span> <span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
                <span class="token keyword">this</span><span class="token punctuation">.</span>right<span class="token punctuation">.</span><span class="token function">add</span><span class="token punctuation">(</span>node<span class="token punctuation">)</span><span class="token punctuation">;</span>
            <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
        <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
    <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
    <span class="token keyword">public</span> <span class="token keyword">void</span> <span class="token function">infixOrder</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
        <span class="token keyword">if</span><span class="token punctuation">(</span><span class="token keyword">this</span><span class="token punctuation">.</span>left<span class="token operator">!=</span>null<span class="token punctuation">)</span><span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
            <span class="token keyword">this</span><span class="token punctuation">.</span>left<span class="token punctuation">.</span><span class="token function">infixOrder</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
        <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
        System<span class="token punctuation">.</span>out<span class="token punctuation">.</span><span class="token function">println</span><span class="token punctuation">(</span><span class="token keyword">this</span><span class="token punctuation">.</span>value<span class="token punctuation">)</span><span class="token punctuation">;</span>
        <span class="token keyword">if</span><span class="token punctuation">(</span><span class="token keyword">this</span><span class="token punctuation">.</span>right<span class="token operator">!=</span>null<span class="token punctuation">)</span><span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
            <span class="token keyword">this</span><span class="token punctuation">.</span>right<span class="token punctuation">.</span><span class="token function">infixOrder</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
        <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
    <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
<span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
</code></pre>
<p><strong>删除</strong></p>
<p><strong>二叉排序树删除共3种情况</strong></p>
<p>1.删除叶子节点<br>2.删除只有一棵子树的节点<br>3.删除含有两颗子树的节点<br><strong>查找节点和该节点的父节点</strong></p>
<pre class=" language-java"><code class="language-java">    <span class="token keyword">public</span> Node <span class="token function">search</span><span class="token punctuation">(</span><span class="token keyword">int</span> value<span class="token punctuation">)</span><span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
        <span class="token keyword">if</span><span class="token punctuation">(</span>value<span class="token operator">==</span><span class="token keyword">this</span><span class="token punctuation">.</span>value<span class="token punctuation">)</span><span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
            <span class="token keyword">return</span> <span class="token keyword">this</span><span class="token punctuation">;</span>
        <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
        <span class="token keyword">if</span><span class="token punctuation">(</span>value<span class="token operator">&lt;</span><span class="token keyword">this</span><span class="token punctuation">.</span>value<span class="token punctuation">)</span><span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
            <span class="token keyword">if</span><span class="token punctuation">(</span><span class="token keyword">this</span><span class="token punctuation">.</span>left<span class="token operator">==</span>null<span class="token punctuation">)</span><span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
                <span class="token keyword">return</span> null<span class="token punctuation">;</span>
            <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
            <span class="token keyword">return</span> <span class="token keyword">this</span><span class="token punctuation">.</span>left<span class="token punctuation">.</span><span class="token function">search</span><span class="token punctuation">(</span>value<span class="token punctuation">)</span><span class="token punctuation">;</span>
        <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span><span class="token keyword">else</span> <span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
            <span class="token keyword">if</span><span class="token punctuation">(</span><span class="token keyword">this</span><span class="token punctuation">.</span>right<span class="token operator">==</span>null<span class="token punctuation">)</span><span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
                <span class="token keyword">return</span> null<span class="token punctuation">;</span>
            <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
            <span class="token keyword">return</span> <span class="token keyword">this</span><span class="token punctuation">.</span>right<span class="token punctuation">.</span><span class="token function">search</span><span class="token punctuation">(</span>value<span class="token punctuation">)</span><span class="token punctuation">;</span>
        <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
    <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
    <span class="token keyword">public</span> Node <span class="token function">searchParent</span><span class="token punctuation">(</span><span class="token keyword">int</span> value<span class="token punctuation">)</span><span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
        <span class="token keyword">if</span><span class="token punctuation">(</span><span class="token punctuation">(</span><span class="token keyword">this</span><span class="token punctuation">.</span>left<span class="token operator">!=</span>null<span class="token operator">&amp;&amp;</span><span class="token keyword">this</span><span class="token punctuation">.</span>left<span class="token punctuation">.</span>value<span class="token operator">==</span>value<span class="token punctuation">)</span><span class="token operator">||</span><span class="token punctuation">(</span><span class="token keyword">this</span><span class="token punctuation">.</span>right<span class="token operator">!=</span>null<span class="token operator">&amp;&amp;</span><span class="token keyword">this</span><span class="token punctuation">.</span>right<span class="token punctuation">.</span>value<span class="token operator">==</span>value<span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
            <span class="token keyword">return</span> <span class="token keyword">this</span><span class="token punctuation">;</span>
        <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span><span class="token keyword">else</span> <span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
            <span class="token keyword">if</span><span class="token punctuation">(</span>value<span class="token operator">&lt;</span><span class="token keyword">this</span><span class="token punctuation">.</span>value<span class="token operator">&amp;&amp;</span><span class="token keyword">this</span><span class="token punctuation">.</span>left<span class="token operator">!=</span>null<span class="token punctuation">)</span><span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
                <span class="token keyword">return</span> <span class="token keyword">this</span><span class="token punctuation">.</span>left<span class="token punctuation">.</span><span class="token function">searchParent</span><span class="token punctuation">(</span>value<span class="token punctuation">)</span><span class="token punctuation">;</span>
            <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span><span class="token keyword">else</span> <span class="token keyword">if</span><span class="token punctuation">(</span>value<span class="token operator">>=</span><span class="token keyword">this</span><span class="token punctuation">.</span>value<span class="token operator">&amp;&amp;</span><span class="token keyword">this</span><span class="token punctuation">.</span>right<span class="token operator">!=</span>null<span class="token punctuation">)</span><span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
                <span class="token keyword">return</span> <span class="token keyword">this</span><span class="token punctuation">.</span>right<span class="token punctuation">.</span><span class="token function">searchParent</span><span class="token punctuation">(</span>value<span class="token punctuation">)</span><span class="token punctuation">;</span>
            <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span><span class="token keyword">else</span> <span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
                <span class="token keyword">return</span> null<span class="token punctuation">;</span>
            <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
        <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
    <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
</code></pre>
<h2 id="平衡二叉树（AVL树）"><a href="#平衡二叉树（AVL树）" class="headerlink" title="平衡二叉树（AVL树）"></a>平衡二叉树（AVL树）</h2><p>平衡二叉树（平衡二叉搜索树）：为一颗空树或它的左右两个字树的高度差的绝对值不超过1，并且左右两个字树都是一颗平衡二叉树。（前提要为二叉排序树）。<br><img src="https://img-blog.csdnimg.cn/3dbd0109dab24644bc682dc8b45941bb.png" alt="在这里插入图片描述"><br>先构建一个二叉排序树，后经过旋转得到平衡二叉树<br><strong>查找高度</strong></p>
<pre class=" language-java"><code class="language-java">   <span class="token keyword">public</span> <span class="token keyword">int</span> <span class="token function">height</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token operator">&amp;</span>#<span class="token number">123</span><span class="token punctuation">;</span>
        <span class="token keyword">return</span> Math<span class="token punctuation">.</span><span class="token function">max</span><span class="token punctuation">(</span>left<span class="token operator">==</span>null<span class="token operator">?</span><span class="token number">0</span><span class="token operator">:</span>left<span class="token punctuation">.</span><span class="token function">height</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">,</span> right<span class="token operator">==</span>null<span class="token operator">?</span><span class="token number">0</span><span class="token operator">:</span>right<span class="token punctuation">.</span><span class="token function">hashCode</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token operator">+</span><span class="token number">1</span><span class="token punctuation">;</span>
    <span class="token operator">&amp;</span>#<span class="token number">125</span><span class="token punctuation">;</span>
</code></pre>
<h1 id="多路查找树"><a href="#多路查找树" class="headerlink" title="多路查找树"></a>多路查找树</h1><h2 id="B树"><a href="#B树" class="headerlink" title="B树"></a>B树</h2><p><img src="https://img-blog.csdnimg.cn/f824cc506dca468093f92901fdca2550.png" alt="在这里插入图片描述"><br><img src="https://img-blog.csdnimg.cn/e1849341def14372a2f0077db117b3ea.png" alt="在这里插入图片描述"></p>
<h2 id="B-树"><a href="#B-树" class="headerlink" title="B+树"></a>B+树</h2><p><img src="https://img-blog.csdnimg.cn/086deb6a13e74da89e32b550fd6765c1.png" alt="在这里插入图片描述"></p>
<h2 id="B-树-1"><a href="#B-树-1" class="headerlink" title="B*树"></a>B*树</h2><p><img src="https://img-blog.csdnimg.cn/ec0130f826c84c2fa967c84fa83042de.png" alt="在这里插入图片描述"></p>

                
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